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Advances in Discrete Differential Geometry

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ISBN: 9783662504468 9783662504475 Year: Pages: 439 DOI: 10.1007/978-3-662-50447-5 Language: English
Publisher: Springer
Subject: Mathematics
Added to DOAB on : 2017-02-03 18:41:25
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This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics.The authors take a closer look at discrete models in differentialgeometry and dynamical systems. Their curves are polygonal, surfacesare made from triangles and quadrilaterals, and time is discrete.Nevertheless, the difference between the corresponding smooth curves,surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, and on pure mathematics and its practical applications. The interaction of these facets is demonstrated by concrete examples, including discrete conformal mappings, discrete complex analysis, discrete curvatures and special surfaces, discrete integrable systems, conformal texture mappings in computer graphics, and free-form architecture.This richly illustrated book will convince readers that this new branch of mathematics is both beautiful and useful. It will appeal to graduate students and researchers in differential geometry, complex analysis, mathematical physics, numerical methods, discrete geometry, as well as computer graphics and geometry processing.

Functional Differential Geometry

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ISBN: 9780262315616 9780262019347 Year: Pages: 248 Language: English
Publisher: The MIT Press
Subject: Mathematics
Added to DOAB on : 2019-01-17 11:41:33
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An explanation of the mathematics needed as a foundation for a deep understanding of general relativity or quantum field theory.Physics is naturally expressed in mathematical language. Students new to the subject must simultaneously learn an idiomatic mathematical language and the content that is expressed in that language. It is as if they were asked to read Les Misérables while struggling with French grammar. This book offers an innovative way to learn the differential geometry needed as a foundation for a deep understanding of general relativity or quantum field theory as taught at the college level.The approach taken by the authors (and used in their classes at MIT for many years) differs from the conventional one in several ways, including an emphasis on the development of the covariant derivative and an avoidance of the use of traditional index notation for tensors in favor of a semantically richer language of vector fields and differential forms. But the biggest single difference is the authors' integration of computer programming into their explanations. By programming a computer to interpret a formula, the student soon learns whether or not a formula is correct. Students are led to improve their program, and as a result improve their understanding.

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geometry --- math

Manifolds - Current Research Areas

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ISBN: 9789535128717 9789535128724 9789535141228 Year: Pages: 160 DOI: 10.5772/63138 Language: English
Publisher: IntechOpen
Subject: Mathematics
Added to DOAB on : 2019-10-03 07:51:49

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Differential geometry is a very active field of research and has many applications to areas such as physics and gravity, for example. The papers in this book cover a number of subjects which will be of interest to workers in these areas. It is hoped that the papers here will be able to provide a useful resource for researchers with regard to current fields of research in this important area.

Differential Geometrical Theory of Statistics

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ISBN: 9783038424253 9783038424246 Year: Pages: XIV, 458 DOI: 10.3390/books978-3-03842-425-3 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Physics (General)
Added to DOAB on : 2017-06-12 12:20:37
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This Special Issue "Differential Geometrical Theory of Statistics" collates selected invited and contributed talks presented during the conference GSI'15 on "Geometric Science of Information" which was held at the Ecole Polytechnique, Paris-Saclay Campus, France, in October 2015 (Conference web site: http://www.see.asso.fr/gsi2015).

Morphological Plant Modeling: Unleashing Geometric and Topological Potential within the Plant Sciences

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Book Series: Frontiers Research Topics ISSN: 16648714 ISBN: 9782889452972 Year: Pages: 296 DOI: 10.3389/978-2-88945-297-2 Language: English
Publisher: Frontiers Media SA
Subject: Science (General) --- Botany
Added to DOAB on : 2018-02-27 16:16:44
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An increasing population faces the growing demand for agricultural products and accurate global climate models that account for individual plant morphologies to predict favorable human habitat. Both demands are rooted in an improved understanding of the mechanistic origins of plant development. Such understanding requires geometric and topological descriptors to characterize the phenotype of plants and its link to genotypes. However, the current plant phenotyping framework relies on simple length and diameter measurements, which fail to capture the exquisite architecture of plants. The Research Topic “Morphological Plant Modeling: Unleashing Geometric and Topological Potential within the Plant Sciences” is the result of a workshop held at National Institute for Mathematical and Biological Synthesis (NIMBioS) in Knoxville, Tennessee. From 2.-4. September 2015 over 40 scientists from mathematics, computer science, engineering, physics and biology came together to set new frontiers in combining plant phenotyping with recent results from shape theory at the interface of geometry and topology. In doing so, the Research Topic synthesizes the views from multiple disciplines to reveal the potential of new mathematical concepts to analyze and quantify the relationship between morphological plant features. As such, the Research Topic bundles examples of new mathematical techniques including persistent homology, graph-theory, and shape statistics to tackle questions in crop breeding, developmental biology, and vegetation modeling. The challenge to model plant morphology under field conditions is a central theme of the included papers to address the problems of climate change and food security, that require the integration of plant biology and mathematics from geometry and topology research applied to imaging and simulation techniques. The introductory white paper written by the workshop participants identifies future directions in research, education and policy making to integrate biological and mathematical approaches and to strengthen research at the interface of both disciplines.

Manifolds II - Theory and Applications

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ISBN: 9781838803094 9781838803100 9781838807160 Year: Pages: 146 DOI: 10.5772/intechopen.75217 Language: English
Publisher: IntechOpen
Subject: Mathematics
Added to DOAB on : 2019-10-03 07:51:53

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Differential geometry is a very active field of research and has many applications to areas such as physics, in particular gravity. The chapters in this book cover a number of subjects that will be of interest to workers in these areas. It is hoped that these chapters will be able to provide a useful resource for researchers with regard to current fields of research in this important area.

Advanced Problems in Mathematics

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Book Series: OBP Series in Mathematics ISBN: 9781783741441 Year: Pages: 186 DOI: 10.11647/OBP.0075 Language: English
Publisher: Open Book Publishers
Subject: Mathematics
Added to DOAB on : 2017-08-22 11:01:03
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" This book is intended to help candidates prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Paper). STEP is an examination used by Cambridge colleges as the basis for conditional offers. They are also used by Warwick University, and many other mathematics departments recommend that their applicants practice on the past papers even if they do not take the examination. Advanced Problems in Mathematics is recommended as preparation for any undergraduate mathematics course, even for students who do not plan to take the Sixth Term Examination Paper. The questions analysed in this book are all based on recent STEP questions selected to address the syllabus for Papers I and II, which is the A-level core (i.e. C1 to C4) with a few additions. Each question is followed by a comment and a full solution. The comments direct the reader’s attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently.&#xD;This book is a must read for any student wishing to apply to scientific subjects at university level and for anybody interested in advanced mathematics.&#xD;"

Kurven – Verstehen – Entwerfen – Berechnen – Darstellen

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ISBN: 9783731506621 Year: Pages: vii, 152 p. DOI: 10.5445/KSP/1000069243 Language: GERMAN
Publisher: KIT Scientific Publishing
Subject: Computer Science
Added to DOAB on : 2019-07-28 18:37:01
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The book is intended for a wide range of readers and contains an introduction to various practically relevant aspects of curves with many illustrations: It offers a treatment of the differential geometric basics, of Bézier and B-spline representations, of rational and algebraic curves, and introduces the reader to some special curves, which are important for applications or historical reasons. Proofs requiring more in-depth mathematical knowledge are dispensed with.

The method of densities for non-isotropic Boolean models

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ISBN: 9783731503293 Year: Pages: 122 p. DOI: 10.5445/KSP/1000045101 Language: ENGLISH
Publisher: KIT Scientific Publishing
Subject: Mathematics
Added to DOAB on : 2019-07-30 20:01:58
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This book deals with the Boolean model, a basic model of stochastic geometry for the description of porous structures like the pore space in sand stone. The main result is a formula which gives in two and three dimensions a series representation of the most important model parameter, the intensity, using densities of so-called harmonic intrinsic volumes, which are new observable geometric quantities.

Palm theory, mass transports and ergodic theory for group-stationary processes

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ISBN: 9783866446694 Year: Pages: IV , 145 p. DOI: 10.5445/KSP/1000022561 Language: ENGLISH
Publisher: KIT Scientific Publishing
Subject: Mathematics
Added to DOAB on : 2019-07-30 20:02:01
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This work is about random measures stationary with respect to a possibly non-transitive group action. It contains chapters on Palm Theory, the Mass-Transport Principle and Ergodic Theory for such random measures. The thesis ends with discussions of several new models in Stochastic Geometry (Cox Delauney mosaics, isometry stationary random partitions on Riemannian manifolds). These make crucial use of the previously developed techniques and objects.

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